From debb6ea07ba68da3d7e6888bae10a3c825423d3e Mon Sep 17 00:00:00 2001
From: Grant Sanderson <grant@3blue1brown.com>
Date: Mon, 12 Mar 2018 17:28:52 -0700
Subject: [PATCH] Simple ManyFormulas scene

---
 active_projects/pi_day.py | 113 ++++++++++++++++++++++++++++++++++----
 1 file changed, 101 insertions(+), 12 deletions(-)

diff --git a/active_projects/pi_day.py b/active_projects/pi_day.py
index fbc58774..f88133d8 100644
--- a/active_projects/pi_day.py
+++ b/active_projects/pi_day.py
@@ -1,3 +1,5 @@
+# -*- coding: utf-8 -*-
+
 from helpers import *
 
 from mobject.tex_mobject import TexMobject
@@ -31,29 +33,32 @@ from mobject.svg_mobject import *
 from mobject.tex_mobject import *
 from topics.graph_scene import *
 
+RESOURCE_DIR = os.path.join(MEDIA_DIR, "3b1b_videos", "π Day 2018")
+
 class PiTauDebate(PiCreatureScene):
     def construct(self):
         pi, tau = self.pi, self.tau
-
         self.add(pi, tau)
 
+        pi_value = TextMobject("3.1415...!")
+        pi_value.highlight(BLUE)
+        tau_value = TextMobject("6.2831...!")
+        tau_value.highlight(GREEN)
+
+
         self.play(PiCreatureSays(
-            pi, "3.1415...!",
+            pi, pi_value,
             target_mode = "angry",
             look_at_arg = tau.eyes,
             # bubble_kwargs = {"width" : 3}
         ))
         self.play(PiCreatureSays(
-            tau, "6.2831...!",
+            tau, tau_value,
             target_mode = "angry",
             look_at_arg = pi.eyes,
             bubble_kwargs = {"width" : 3, "height" : 2},
         ))
-        self.wait(2)
-        self.play(
-            RemovePiCreatureBubble(pi),
-            RemovePiCreatureBubble(tau),
-        )
+        self.wait()
 
         # Show tau
         circle = Circle(color = YELLOW, radius = 1.25)
@@ -82,7 +87,11 @@ class PiTauDebate(PiCreatureScene):
             **kwargs
         )
 
-        self.play(ShowCreation(radius), Write(one))
+        self.play(
+            ShowCreation(radius), Write(one),
+            RemovePiCreatureBubble(pi),
+            RemovePiCreatureBubble(tau),
+        )
         self.play(
             tau.change, "hooray",
             pi.change, "sassy",
@@ -138,9 +147,89 @@ class PiTauDebate(PiCreatureScene):
         tau.to_edge(DOWN).shift(4*RIGHT)
         return VGroup(pi, tau)
 
-
-
-
+class HartlAndPalais(Scene):
+    def construct(self):
+        hartl_rect = ScreenRectangle(
+            color = WHITE,
+            stroke_width = 1,
+        )
+        hartl_rect.scale_to_fit_width(SPACE_WIDTH - 1)
+        hartl_rect.to_edge(LEFT)
+        palais_rect = hartl_rect.copy()
+        palais_rect.to_edge(RIGHT)
+
+        tau_words = TextMobject("$\\tau$ ``tau''")
+        tau_words.next_to(hartl_rect, UP)
+
+        hartl_words = TextMobject("Michael Hartl's \\\\ ``Tau manifesto''")
+        hartl_words.next_to(hartl_rect, DOWN)
+
+        palais_words = TextMobject("Robert Palais' \\\\ ``Pi is Wrong!''")
+        palais_words.next_to(palais_rect, DOWN)
+
+        for words in hartl_words, palais_words:
+            words.scale(0.7, about_edge = UP)
+
+        three_legged_creature = ThreeLeggedPiCreature(height = 1.5)
+        three_legged_creature.next_to(palais_rect, UP)
+
+        # self.add(hartl_rect, palais_rect)
+        self.add(hartl_words)
+        self.play(Write(tau_words))
+        self.wait()
+        self.play(FadeIn(palais_words))
+        self.play(FadeIn(three_legged_creature))
+        self.play(three_legged_creature.change_mode, "wave")
+        self.play(Blink(three_legged_creature))
+        self.wait()
+
+class ManyFormulas(Scene):
+    def construct(self):
+        formulas = VGroup(
+            TexMobject("\\sin(x + \\tau) = \\sin(x)"),
+            TexMobject("e^{\\tau i} = 1"),
+            TexMobject("n! \\approx \\sqrt{\\tau n} \\left(\\frac{n}{e} \\right)^n"),
+            TexMobject("c_n = \\frac{1}{\\tau} \\int_0^\\tau f(x) e^{inx}dx"),
+        )
+        formulas.arrange_submobjects(DOWN, buff = MED_LARGE_BUFF)
+        formulas.to_edge(LEFT)
+
+        self.play(LaggedStart(FadeIn, formulas, run_time = 3))
+
+        circle = Circle(color = YELLOW, radius = 2)
+        circle.to_edge(RIGHT)
+        radius = Line(circle.get_center(), circle.get_right())
+        radius.highlight(WHITE)
+
+        angle_groups = VGroup()
+        for denom in 8, 4, 3:
+            radius_copy = radius.copy()
+            radius_copy.rotate(TAU/denom, about_point = circle.get_center())
+            arc = circle.copy()
+            arc.set_stroke(RED, width = 4)
+            arc.pointwise_become_partial(circle, 0, 1./denom)
+            mini_arc = arc.copy()
+            mini_arc.set_stroke(WHITE, 2)
+            mini_arc.scale(0.2, about_point = circle.get_center())
+            tau_tex = TexMobject("\\tau/%d"%denom)
+            tau_tex.next_to(
+                mini_arc, 
+                mini_arc.point_from_proportion(0.5) - circle.get_center()
+            )
+            angle_group = VGroup(radius_copy, mini_arc, tau_tex, arc)
+            angle_groups.add(angle_group)
+
+
+        angle_group = angle_groups[0]
+        self.play(*map(FadeIn, [circle, radius]))
+        self.play(
+            FadeIn(angle_group),
+            circle.fade, 0.25,
+        )
+        self.wait()
+        for group in angle_groups[1:]:
+            self.play(Transform(angle_group, group, path_arc = TAU/8))
+            self.wait()